Concentration distribution and spatial moments of moving macromolecules undergoing isomerization

✍ Scribed by M. K. Killalea; B. J. McCoy

• Publisher: Wiley (John Wiley & Sons)
• Year: 1980
• Tongue: English
• Weight: 503 KB
• Volume: 19
• Category: Article
• ISSN: 0006-3525
• DOI: 10.1002/bip.1980.360191014

✦ Synopsis

Abstract

Expressions for zeroth, first, and second spatial moments are obtained for diffusing macromolecules A and B that move due to an external field and undergo reversible isomerization, switching back and forth according to first‐order kinetics. In addition, expressions for third and fourth moments are derived for the special case of equal diffusion coefficients, equal rate constants, and equal but opposite velocities. The initial conditions are arbitrary amounts of A or B concentrated in an infinitesimally narrow region. The moments are computed from derivatives of the Fourier‐transformed concentration profiles of A and B. The moments are used in an expansion in term of Hermite polynomials, the Gram‐Charlier expansion, to construct the concentration profiles of A or B or A and B together. The examples presented show that a few terms of the expansion, for which explicit expressions are given, can give tolerable accuracy if the velocity is not too large and the rate constants and diffusion coefficient are not too small. The expansion can be used to determine when the profiles are unimodal.